1. Field of the Invention
The present invention relates generally to the measurement of thickness and orientation of an article, and more particularly to a method and apparatus for determining the anisotropic orientation and thickness of an article formed of an anisotropic material.
2. Description of the Related Art
It is known that anisotropic materials such as those formed of a single metallic crystal can offer significant advantages in certain engineering applications. For example, a structural component made of a single crystal may be significantly stronger than a component formed of a polycrystalline material, due to the relatively weak junction between crystals or "grains" in the polycrystalline material. The absence of such junctions in an anisotropic, single crystal component is especially important in high temperature applications, where the strength of the junction is further diminished.
In using anisotropic materials for manufacturing, however, it is often important to ensure that the material is properly aligned in its finished state. Since the material properties can be highly directionally dependent, small deviations in crystal orientation can result in significant changes in the mechanical response of the component and its ability to perform as designed, for example in high temperature or high stress applications. With the advent of anisotropic, single crystal components in critical, load bearing areas, the ability to characterize orientation nondestructively is important to ensuring the quality of such components.
Another area in which it is often important to ensure the proper alignment of an anisotropic component is in machining. Many structural materials, while statistically isotropic in their original form, are produced in rolling or extrusion operations, which results in an anisotropy due to a preferential alignment in the grain structure. For some of these materials, e.g. titanium, knowledge of the material anisotropy may be critical to the efficient machining of the component.
Conventional methods for determining the crystal orientation of an isotropic material typically utilize x-ray diffraction, in which the interference pattern of diffracted x-ray radiation is used to reconstruct the crystal orientation. While x-ray diffraction methods are generally accurate and nondestructive, each measurement is very time consuming. In addition, only the material properties at the surface of the article are measured. X-ray diffraction methods are therefore impractical unless it is feasible to cut a small portion from the sample for testing, in which case the method is no longer nondestructive.
Another known method for determining the crystal orientation in an article formed of a single crystal material is described in Green et al, Ultrasonic Orientation Determination of Single Crystals, 41 Journal of the Accoustical Society of America 84 (1967). This method involves compiling a table of values for the velocities of shear and longitudinal waves propagated a priori through a sample of the single crystal material. The velocity values are plotted on a standard stereographic triangle as a function of the direction of propagation, as shown for example in FIGS. 1a-1c, where FIG. 1a is a longitudinal wave, FIG. 1b is a slow shear wave and FIG. 1c is a fast shear wave. Since every distinct crystal orientation is associated with a unique combination of longitudinal and shear wave velocities, a measurement of these values on the article to be tested can be used to find the crystal orientation of the article by overlaying any two of the three stereographic triangles. The velocities of the waves through the article may be obtained by measuring the transit times of longitudinal and shear waves reflected off the back surface of the article.
The Green et al method, however, requires that the thickness of the article be known independently to calculate velocity, as only transit time is measured. The method is unavailable, therefore, in applications where the thickness cannot be measured. Although methods for nondestructive measurement of the thickness of an article, e.g. ultrasonic methods, are well known, such devices typically utilize a known velocity of sound propagation in conjunction with a measured transit time to extract the distance traveled by the wave, i.e., the thickness. These devices, however, are generally applicable only to isotropic media, and can be very inaccurate when the velocity of sound changes with the propagation direction, as in an anisotropic material. Thus, when both the crystal orientation and the thickness are unknown, a new approach is needed to avoid errors arising from the intrinsic variation in velocity due to anisotropy.
Another significant shortcoming of the Green et al method is that it is a graphical method which involves overlaying two stereographic triangle plots and finding an intersection point between two velocity curves to determine the crystal orientation. As such, there is an inherent uncertainty associated with manually locating the contour intersection points on the two stereographic triangles. This places stringent limits on the precision in the velocity measurement needed to orient a typical crystal, particularly if the degree of anisotropy is relatively small. Green et al estimate that the acoustic velocities must be measured to within an accuracy of 0.1% for the method to be useful. This degree of measurement accuracy may be difficult to achieve in many applications. This shortcoming, along with the cumbersome nature of the stereographic plot manipulations, has precluded its use in practice.